After MK Tamar Zandberg's (Meretz) law proposal for operating public transporation on Shabbos was voted down, she proposed a new law.

According to Zandberg's proposal, government issued cars would not be allowed to be used on Shabbos. Meaning, ministers and anyone else issued a government car would nopt be allowed to drive that car on Shabbos. if they have a personal privately owned car, they could drive that, but not the one issued from the government.

Zandberg explained that the Ministers should show responsibility and set themselves as a personal example to the public and let their government issued cars sit idle on Shabbos. These cars are financed by the public, and if the public can't have public transportation,  on their rest day and on holidays, the ministers should not have this type of public transportation either. This would lessen the inequality, she says.

Zandberg adds that the law would include a clause that the law itself would expire if public transportation would ever be allowed on Shabbos.
source: Haredim10

I dont know that a few dozen cars taken off the road is significant enough to lessen the inequality, but the other points are fair. Not only are those a form of public transportation, and if they are voting against it for the general public they themselves shouldn't benefit from it when they dont allow others to, but in general ministers are encouraged to not desecrate Shabbos publicly. Every time it happens a big deal is made and the minister issues an apology or explanation.... just dont let them use the car on Shabbos for private business. Obviously if there is a crisis with an urgent need requiring governmental intervention it would eb allowed, but not for general use.